But finite life expectancies effectively act as a cap on that process. In the very best case, you only have about half a century to compound wealth.
Modern America is not very conducive to preserving intergenerational wealth. Of the top ten richest Americans, only one is not a first-generation billionaire. Rockefeller despite amassing an enormous fortune, equivalent to $400 billion today, does not have any heirs in the top 100 a century later.
There's a number of factors at play here. First, US estate taxes tend to be consistently high around 35%+ and pretty hard to avoid. Second, unlike traditional aristocracies, the scions of American capitalism rarely arrange marriages with other prominent families. Consequently dynastic wealth almost always gets diluted by 50% or more every generation. Third, US GDP growth has historically averaged pretty high around 3% per annum. The relative size of a fortune to the broader economy is constantly shrinking per year.
These factors combine to make the relative size of a dynastic fortune shrink by about 85% per generation. Assuming a generation gap of 30 years, you'd have to achieve consistent real returns of 7% a year. And that's assuming no loss of capital due to consumption, philanthropy, divorce, capital gains tax, dividend taxes or fraud.
Over the past century, equities have only averaged a 6% real rate of return. Unless you have significant financial or business acumen, sustainably beating the stock market on a large portfolio over decades is virtually impossible. On an inter-generational basis that talent is very unlikely to be present in every scion. A dynasty with a penchant for risk-taking is far more likely to blow their fortune by some idiot son along the way.